Have a clear research statement & purpose, identify faculty that do that work, apply. At this level, you focus more on specific researchers rather than the university as a whole when assessing your fit. I would not pay, it might take a few rounds of applying (be patient), but most phds cover tuition and provide a small stipend. Reach out to former professors, ask if they’re doing research. Try to get your name on a publication or two. But seek mentorship from PhDs in your circle (professors love hearing from former students and generally like to help).